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ornery_chemist@mander.xyz ⁨1⁩ ⁨month⁩ ago

Isn’t the squaring actually multiplication by the complex conjugate when working in the complex plane? i.e., √((1 - 0 i) (1 + 0 i) + (0 - i) (0 + i)) = √(1 + - i^2^) = √(1 + 1) = √2. I could be totally off base here and could be confusing with something else…

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diaphanous@feddit.org ⁨1⁩ ⁨month⁩ ago
I think you’re thinking of taking the absolute value squared, |z|^2 = z z*

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- candybrie@lemmy.world ⁨1⁩ ⁨month⁩ ago
  Considering we’re trying to find lengths, shouldn’t we be doing absolute value squared?
  
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HexesofVexes@lemmy.world ⁨1⁩ ⁨month⁩ ago
Almost:

Lengths are usually reals, and in this case the diagram we can use assume that A is the origin wlog (badly drawn vectors without a direction)

Next we convert the vectors into lengths using the abs function (root of conjugate multiplication). This gives us lengths of 1 for both.

Finally, we can just use a Euclidean metric to get out other length √2.

Squaring isn’t multiplication by complex conjugate, that’s just mapping a vector to a scalar (the complex | x | function).

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